normalized (because of (REF )) by the surface area of
\({\mathbb {S}},\)  which is \(\frac{2 \pi ^{d/2}}{\Gamma (d/2)}.\) 
It is known (see [1]}), that the surface area of this spherical
cap equals
\(\frac{\pi ^{d/2}}{\Gamma (d/2)}J_{2h-h^2}\left(\frac{d-1}{2},\frac{1}{2}\right)=\frac{\pi ^{d/2}}{\Gamma (d/2)}J_{\rho ^2/x_1^2}\left(\frac{d-1}{2},\frac{1}{2}\right),\) 
